BUS 421: Comparative Pricing Model Analytics CAL 2 Dr. Gordon H Dash WinORS-2020 version (FRAME) Deliverable submissions must be made by email: [email protected] Due Date: See class audit blog

LEARNING OBJECTIVES and OUTCOMES The overall objective of this CAL is to introduce students to the computational aspects of using two classic option pricing models. Classic means that the focus is on the foundation models as presented in any introductory presentation within the computational literature (yes, there are extensions, but they are not covered in this assignment). The assignment features computations using the Binomial and Black and Scholes option pricing models (MBOPM & BSOPM, respectively). In addition to learning to compute and interpret the ‘theoretically correct price’ of an option, the assignment features a full development on ‘best use’ of computed ratios and related option .

Specific Learning Objectives: 1. To introduce students to classic option pricing models. 2. To introduce students to the functional differences between the Binomial option pricing model and its related rival, the Black and Scholes option pricing model. 3. To interpret lattice output generated by the MBOPM 4. To compare: historical , realized volatility, and .

RESOURCES, TOOLS, and SETUP 1. ARMDAT – Chapters 2, 4 & 5 2. WinORS-2020 on FRAME 3. MONOSNAP 4. Videos and other online material as required on www.ARMDAT.com . 5. Report template available on FRAME: Template for CAL2 Report.docx

ASSIGNMENT

Obtain Model Input Data and Calculate 1. Go to Yahoo/Finance (or your favorite web portal). Go to the options page for your ticker. Pick a Call and that has a traditional date with at least 14 days left to expiration. Locate the Last Trade price and IV for both the call and put.

Parameter Value (example) Enter on Calc. Row S Observed Equity Price X Observed Price – Choose Historical Volatility (V) Computed (see. Pt 2) Std Dev / Volatility (%) Rf Average of ^IRX Risk Free Rate (%) T (calculator will present based Select radio button: Measured in days on traditional expiration date) Expiration Month/Year (D) in percent Observed Annual Yield (%) Call-Last Trade Price Observed Price Put-Last Trade Price Observed Put Option Price Call-IV Observed --- Put-IV Observed ---

2. Return to the spreadsheet used in CAL 1. Using the time series of (log-differenced) returns for the chosen ticker calculate an estimate of the annualized volatility (standard deviation). Forgot how? Refer to chapter 2, the sections on: a) Annualized historical volatility; use the annualized HV as an estimate for StdDev / Volatility (%) in the calculator) and b) Distributional Properties (second moment). Also see the Fx Excel equation sections in the Chapter 2 for WinORS specific formula.

Use the WinORS-2020 Options Calculator to solve both the MBOPM and BSOPM for the theoretically correct option prices and all other calculated terms. Use menu option: Data | Calculators | PC Based | Option and solve the following models (capture output as needed for paste into WriteORS): 1. MBOPM – American 2. BSOPM – European

Deliverable – Reporting Requirements After examining the two alternative solutions, it should be readily apparent that option Greeks differ by model and . 1. Insert Table 1. Make sure information on your focus ticker is followed by information for all other tickers in the group. 2. For the American style, which calculator computed theoretical option price (call or put) is closer to the Yahoo reported price after making the early exercise premium adjustment? (see: ARMDAT 5, section: Pricing American Style Options). Compute and report IVal as a check on Time Value (theoretical and actual) for both the call and put. (Insert Table 2 and write a small narrative comparing the focus ticker to the group tickers). 3. Compare: a. the computed implied volatility produced by the calculator to the implied volatility observed on Yahoo. (Insert Table 2 and write a narrative) b. implied volatility to the annualized historical volatility 4. All hedge ratio reporting is presented as Delta. a. Compare the computed hedge ratios for MBOPM and BSOPM. How much variation (or similarity) is there among the computed hedge ratios? b. Interpret Dual Delta and the P(ITM). (Insert Table 3 and write a small narrative comparing all tickers). 5. Assume the annualized Std Dev/Volatility increases by 1%. What impact does this increase have on: a. Call and put theoretical prices (up, down, the same)? b. Call hedge ratio c. Lambda@IV for both calls and puts -- What can you say about the sensitivity of the option premium to implied volatility changes. 6. Reference is made to the captured MBOPM lattice. The lattice reports the theoretically correct price at the computed step. The following is only for the focus ticker. a. Refer to either the 3rd, 4th, or 5th step. Locate an OTM option with a positive price in the value box. If the option is OTM with an IVal = 0, then what does the positive price represent. b. At the far-right end of the node, given your understanding of volatility for this how “believable” is the projected uptick S for the given tick (day) time? c. Same question, but for the projected downtick of S.

The Submission Attach to the submission email (one email per group) ALL of the following: a. The group’s Report / Deliverable in either a DOCX or PDF format. The latter is preferred. The Report is the formal document and must be organized, proof-read and styled as such. b. Mail to [email protected] c. Subject line of the email: BUS421 Group # - CAL1 Submission. Make sure you replace # with your group number.

Last Edit: 26-Feb-2019; 04-March-2019; 10-Oct-2019